The equation of line L1 is y= 3x - 2

In the form y   = mx + b   .......the slope is  "m"

So  in the line

y =  3x  -  2         the slope  =  3

Now........ line 2  is

3y - 9x + 5  = 0      ....we want to get y by itself

Add 9x to both sides, subtract 5 from both sides

3y   =  9x  - 5         divide both sides by 3

y  =  3x  -  5/3      and note that the slope is exactly the same as the first one

And two lines with the same slope are always parallel